Let matrix A = \begin{pmatrix} 2 & 5 \\ -1 & 3 \end{pmatrix} and matrix B = \begin{pmatrix… — ACT

Let matrix $A = \begin{pmatrix} 2 & 5 \\ -1 & 3 \end{pmatrix}$ and matrix $B = \begin{pmatrix} 4 & -2 \\ 3 & 1 \end{pmatrix}$ . If matrix $C = 2A + 3B$ , what is the value of the entry in the second row and first column of matrix $C$ ?

Answer: 7

Answer

The entry in the second row and first column of matrix

C

is 7.

The entry in the second row, first column of matrix

C

, denoted as

c_{2,1}

, is calculated by multiplying the corresponding entry in matrix

A

(

a_{2,1} = -1

) by 2 and the corresponding entry in matrix

B

(

b_{2,1} = 3

) by 3, and then adding the results:

2(-1) + 3(3) = -2 + 9 = 7

Step-by-Step Solution

Locate the element in the second row, first column of both matrices

A

and

B

The element in the second row, first column of

A

(designated

a_{2,1}

) is

-1

, and the element in the second row, first column of

B

(designated

b_{2,1}

) is

3

To find a specific entry in the resulting matrix

C = 2A + 3B

, we perform the scalar multiplication and addition operations on the corresponding entries in the same position of matrices

A

and

B

Multiply the corresponding elements by their respective scalar factors.

For matrix

A

2 \times (-1) = -2

. For matrix

B

3 \times 3 = 9

Scalar multiplication requires multiplying each individual entry of a matrix by the given scalar factor.

Add the two resulting values to find the entry for matrix

C

-2 + 9 = 7

Matrix addition is performed by adding the corresponding elements of the matrices.

Key Concept

Matrix scalar multiplication and addition of corresponding elements

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic